Discrete Dynamics in Nature and Society
Volume 2007 (2007), Article ID 54861, 15 pages
Research Article

Permanence and Stability of an Age-Structured Prey-Predator System with Delays

Liming Cai,1,2 Xuezhi Li,1 Xinyu Song,1 and Jingyuan Yu2

1College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, Henan, China
2Beijing Institutes of Information and Control, Beijing 100037, China

Received 15 March 2007; Accepted 30 April 2007

Copyright © 2007 Liming Cai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An age-structured prey-predator model with delays is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, permanence, and stability are analyzed. By using the persistence theory for infinite-dimensional systems, the sufficient conditions for the permanence of the system are obtained. By constructing suitable Lyapunov functions and using an iterative technique, sufficient conditions are also obtained for the global asymptotic stability of the positive equilibrium of the model.